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Card Back

An interactive lesson Card Front


Here is a tile:



On this tile we'll draw a circle:



If we rotate this tile, it will always look the same:
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Here is another tile, If we rotate this tile, it changes:

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This tile has 2 orientations

     

Combining tiles like these allow for interesting patterns

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This is what’s called a Truchet Tile, after Sebastien Truchet who wrote a paper called “Memoir sur les Combinasions” for Memoir de l’Académie Royale des Sciences in 1704, in which he extensively outlines the types of patterns one can achieve with orientable tiles, though the tiles he used for his examples look like this, which are also pretty fun:

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Something you might notice about truchet tiles is that while they may not have rotational symmetry, they do have at least 1 axis of reflective symmetry:

    

it is this quality that allows the shapes on the tile to line up with the shapes on the adjacent tile, regardless of orientation.

Let’s make a tile that doesn’t have this quality:


I call this one the batwing

Can you make these tiles flow into each other like truchet tiles?
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Yes... But why?

Let’s have another look at this tile:

The reason this tile patterns into itself is because the shapes on it are designed such that they “enter” and “exit” in the same location regardless of the orientation of the tile.
In this tile I purposely left 1 out of 4 sides closed; the tile won’t flow into itself on this side. This allows us to make pattern schemes that are unlike anything truchet tiles could achieve:


In this example I’ve made a 5-tile repeatable pattern

An easy way to design a tile like the batwing tile is to combine the corners of existing symmetrical tiles:



Whoever is reading this should try and make a tile like this right now and send it to me :^)

What else can tiles do?

Glad you asked, here are some tiles that can be used to make words:



It was actually just these 4 tiles that were used to make the title at the top of the page:



When your mouse hovers over the title at the top of the page, what you’re seeing are the individual tiles of each word rotating by 90 degrees.


That’s all the stuff I’ve learned about tiles so far, I’m sure I’ll come up with more later.

Thanks for reading!

August 2020